Using dominance property, solve the game whose payoff matrix is
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Prove that the dual of dual of a LPP is primal LPP.
Solve the following LPP using two-phase method.
Min Z = -3x - 2y - 2z
s.t. 5x + 7y + 4z > 7
- 4x + 7y + 5z > -2
3x + 4y - 6z > 29 / 7
x, y, z > 0.
Find an initial basic feasible solution to the following transportation problem by the North-West corner method. Check whether your solution is optimal.
| 6 | 4 | 1 | 5 | 14 |
| 8 | 9 | 2 | 7 | 16 |
| 4 | 3 | 6 | 2 | 5 |
| 6 | 10 | 15 | 4 |
For the following matrix game, write down the equivalent LPPs for solving the game.
B
For the transportation problem given below. Check whether the given basic feasible solution is optimal. If not, modify the given solution and find an optimal solution and the optimal value for the problem.
| 6 | 1 (25) | 9 | 3 (45) | 70 |
| 11 | 5 (5) | 2 (50) | 8 | 55 |
| 10 (85) | 12 (5) | 4 | 7 | 90 |
| 85 | 35 | 50 | 45 |
A company has 5 jobs to be processed by 5 mechanics. The following table gives the return in rupees when the ith job is assigned to the jth mechanic ( i, j = 1,2,....5) . How should the jobs be assigned to the mechanics so as to maximize the overall return?
| 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|
| 1 | 22 | 28 | 30 | 18 | 30 |
| 2 | 30 | 34 | 18 | 11 | 26 |
| 3 | 31 | 17 | 23 | 20 | 27 |
| 4 | 12 | 28 | 31 | 26 | 26 |
| 5 | 19 | 23 | 30 | 25 | 29 |
A businessman needs 5 cabinets, 12 desks and 18 shelves cleaned out. He has two part time employees, Rashid and Ruby. Ruby can clean 1 cabinet, 3 desks and 3 shelves in a day while Rashid can clean 1 cabinet, 2 desks and 6 shelves in one day. Rashid is paid Rs.22 per day and Ruby is paid Rs.25 per day. In order to minimize the cleaning costs, for how many days should Rashid and Ruby be employed? Formulate the problem as a linear programming problem and find its solution by simplex method.